Geodesics on a torus of revolution. This dynamical system
is integrable as in any surface of revolution.

The primary caustic can already be complicated for
a rotationally symmetric torus of revolution. There are
directions, in which the geodesic winds around the torus
several times before the Jacobi field reaches a zero.
For these pictures, 120'000 geodesics have been started from
one point and integrated until time 2PI. Always
the first point was marked, where the Jacobi field is zero.